On second Noether's theorem and gauge symmetries in Mechanics

2005/11/07 by José F. Cariñena, Jose F Carinena, Joan-Andreu Lazaro-Cami +6
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computational Physics and Python Applications #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.math/0511180

arxiv created 2005/11/07 · openalex publication_date 2005/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the geometric formulation of the second Noether's theorem in time-dependent mechanics. The commutation relations between the dynamics on the final constraint manifold and the infinitesimal generator of a symmetry are studied. We show an algorithm for determining a gauge symmetry which is closely related to the process of stabilization of constraints, both in Lagrangian and Hamiltonian formalisms. The connections between both formalisms are established by means of the time-evolution operator.

Related

• Dynamical Systems with First- and Second-Class Constraints and the Second Noether Theorem
• Symmetries of the dynamics and Noether theorem in classical mechanics
• Geometry and Dynamics with Time-Dependent Constraints
• The commutativity principle and lagrangian symmetries
• Noether's theorem, the stress-energy tensor and Hamiltonian constraints